src/ZF/ex/Term.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/Term.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,66 @@
+(*  Title: 	ZF/ex/term.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Datatype definition of terms over an alphabet.
+Illustrates the list functor (essentially the same type as in Trees & Forests)
+*)
+
+structure Term = Datatype_Fun
+ (val thy = List.thy;
+  val rec_specs = 
+      [("term", "univ(A)",
+	  [(["Apply"], "[i,i]=>i")])];
+  val rec_styp = "i=>i";
+  val ext = None
+  val sintrs = ["[| a: A;  l: list(term(A)) |] ==> Apply(a,l) : term(A)"];
+  val monos = [list_mono];
+  val type_intrs = [SigmaI,Pair_in_univ, list_univ RS subsetD, A_into_univ];
+  val type_elims = []);
+
+val [ApplyI] = Term.intrs;
+
+(*Induction on term(A) followed by induction on List *)
+val major::prems = goal Term.thy
+    "[| t: term(A);  \
+\       !!x.      [| x: A |] ==> P(Apply(x,Nil));  \
+\       !!x z zs. [| x: A;  z: term(A);  zs: list(term(A));  P(Apply(x,zs))  \
+\                 |] ==> P(Apply(x, Cons(z,zs)))  \
+\    |] ==> P(t)";
+by (rtac (major RS Term.induct) 1);
+by (etac List.induct 1);
+by (etac CollectE 2);
+by (REPEAT (ares_tac (prems@[list_CollectD]) 1));
+val term_induct2 = result();
+
+(*Induction on term(A) to prove an equation*)
+val major::prems = goal (merge_theories(Term.thy,ListFn.thy))
+    "[| t: term(A);  \
+\       !!x zs. [| x: A;  zs: list(term(A));  map(f,zs) = map(g,zs) |] ==> \
+\               f(Apply(x,zs)) = g(Apply(x,zs))  \
+\    |] ==> f(t)=g(t)";
+by (rtac (major RS Term.induct) 1);
+by (resolve_tac prems 1);
+by (REPEAT (eresolve_tac [asm_rl, map_list_Collect, list_CollectD] 1));
+val term_induct_eqn = result();
+
+(**  Lemmas to justify using "term" in other recursive type definitions **)
+
+goalw Term.thy Term.defs "!!A B. A<=B ==> term(A) <= term(B)";
+by (rtac lfp_mono 1);
+by (REPEAT (rtac Term.bnd_mono 1));
+by (REPEAT (ares_tac (univ_mono::basic_monos) 1));
+val term_mono = result();
+
+(*Easily provable by induction also*)
+goalw Term.thy ([e-mail]_defs) "term(univ(A)) <= univ(A)";
+by (rtac lfp_lowerbound 1);
+by (rtac (A_subset_univ RS univ_mono) 2);
+by (safe_tac ZF_cs);
+by (REPEAT (ares_tac [Pair_in_univ, list_univ RS subsetD] 1));
+val term_univ = result();
+
+val term_subset_univ = standard
+    (term_mono RS (term_univ RSN (2,subset_trans)));
+